Abstract
We consider nonnegative solutions of the semilinear parabolic equation u t —u xx + u p = 0, -∞<x< +∞, t>0, 0<p<l, which vanish at the extinction point x = 0 at a time t = T. By means of formal methods, we derive a family of asymptotic expansions for solutions and interface curves (these last separating the regions where u = 0 and u> 0), as (x,t) approaches (0,T).
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© 1992 Springer Science+Business Media New York
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Galaktionov, V.A., Herrero, M.A., Velázquez, J.J.L. (1992). The Structure of Solutions near an Extinction Point in a Semilinear Heat Equation with Strong Absorption: A Formal Approach. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_16
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DOI: https://doi.org/10.1007/978-1-4612-0393-3_16
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6741-6
Online ISBN: 978-1-4612-0393-3
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